AP EAMCET · Maths · Permutation Combination
If \({ }^n C_{r-1}=36,{ }^n C_r=84\) and \({ }^n C_{r+1}=126\), then the value of \(n r^2\) is
- A \(243\)
- B \(9\)
- C \(27\)
- D \(81\)
Answer & Solution
Correct Answer
(D) \(81\)
Step-by-step Solution
Detailed explanation
\(\frac{{ }^n C_r}{{ }^n C_{r-1}}=\frac{84}{36}\) \(\Rightarrow \frac{\frac{n !}{(n-r) ! r !}}{\frac{n !}{(r-1) !(n-r+1) !}}=\frac{7}{3}\) \(\begin{array}{ll}\Rightarrow & \frac{n-r+1}{r}=\frac{7}{3} \\ \Rightarrow & 3 n-3 r+3=7 r\end{array}\)…
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